It has been a while since I have checked in here. With the Lubuntu LTS version I had been using on this Inspiron 6000 laptop nearing end of life, I decided to give Debian Stretch with LXDE desktop a try. The intel video driver is a bit newer, but I have the same problem with the Pale Moon Preferences Menu as before.

Thank you so much for the research and the solution to this problem.
I tried it on my old Dell Latitude D610 laptop. It works like a charm.
I have been hoping for a solution since August. Now, out of nowhere, it appears.
I am truly impressed.
Thanks again.

Created a file (as root) called /etc/X11/xorg.conf.d/20-intel.conf with the following contents: ...

I tried to do the same on my 13 years old HP laptop running Linux Mint 19.1 (see https://forum.palemoon.org/viewtopic.php?f=37&t=20713#p159685), but the OS refuses to copy anything to the directory /etc/X11/xorg.conf.d/. Instead Linux says that I am not the "owner" of that directory and I don't have the permission to copy. I am a 100-percent newbie to linux and thus I really don't know what I else could try to run my favorite browser without this annoying "bug" on that old machine (which has no problems with any other application I have tested). Could you please tell me how I can get Linux' permission to copy the file 20-intel.conf to the directory /etc/X11/xorg.conf.d/?

I might be able to help you even though I am a newbe too.
I am using antiX linux.
I made the file as instructed and saved it to the desktop. I right clicked on the file and chose Properties. Then, I selected Execute to the permissions.
Then, I opened File Manage and opened the File menu, and selected Root Window.
Then, I found the file 20-intel.conf in desktop and copied it to clip board.
Then, I found /etc/X11/xorg.conf.d and pasted the file in the folder.
Then, close the Root Window and do a restart.

Many thanks! I followed your instructions on my old HP 32-bit laptop running Mint 19.1 and now Palemoon 28.3.1 preferences are working again and the Media tab has also re-appeared in the Page Info dialog.

A workaround is to open the addon preferences window, THEN maximize, restore, AGAIN maximize, restore THEN it seems to work.
This will also make the browser preferences window work if animateFadeIn is false.